Results from search using profile cannot be added to events

As identified in this forum thread:
http://forum.civicrm.org/index.php?topic=12046

When searching using basic or advanced search with a custom search profile selected, the 'Add contacts to event' search results task does not work. Selecting some search results and 'Add contacts to event' generates a 'Could not find valid cid' error on the multiple participants add form.

Steps to reproduce this on the 3.1 demo site:
1) On the menu, select Administer->Customize->CiviCRM profile
2) Create a new profile used for search results and tick it active
3) Create a field for this profile (e.g. street address) used for 'Contacts', with visibility: 'Public Pages' and 'Results column' ticked.
4) Go to advanced search, tick 'Individuals' and then under the 'Search views' box in the top right, choose the custom profile and click search
5) Select some contacts from the search results and choose 'Add Contacts to Event' from the search tasks and click the 'Go' button.
6) See the resulting error!